Question

If r4=r1+r2+r3, which of the vectors are linearly dependent?
a)r1
b)r3
c)r4
d)r2

Answer 1

c) r4
If you can represent the sum of given vectors r1,r2 and r3 by a single vector r4 i.e. r4= r1+ r2+ r3.
Then you can say r4 is linearly dependent on r1, r2 and r3 and that r1, r2 ,r3 and r4 constitute a linearly dependent set of vectors. On the other hand r1, r2 and r3 are linearly independent vectors